| Title: | Minimal surfaces with symmetries |
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| Authors: | ID Forstnerič, Franc (Author) |
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| Files: |  URL - Source URL, visit https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12590
 PDF - Presentation file, download (483,34 KB)
MD5: DDCD746711142D30954B69AEDC137F4C
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space ${\mathbb R}^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\to{\mathbb R}^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on ${\mathbb R}^n$ by rigid transformations. |
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| Keywords: | Riemann surfaces, minimal surfaces, G-equivariant conformal minimal immersion |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.03.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 32 str. |
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| Numbering: | Vol. 128, iss. 3, [article no.] e12590 |
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| PID: | 20.500.12556/DiRROS-18392  |
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| UDC: | 517.5 |
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| ISSN on article: | 0024-6115 |
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| DOI: | 10.1112/plms.12590 |
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| COBISS.SI-ID: | 188644867 |
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| Note: |
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| Publication date in DiRROS: | 13.03.2024 |
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| Views: | 1019 |
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| Downloads: | 587 |
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